Adjacent and nonadjacent angles: how to tell them apart
When several angles meet at the same point, it helps to look at one pair at a time. We’ll use the sides of each angle and the space between them to decide which pairs are adjacent.
What makes two angles adjacent?
Adjacent angles share a vertex and exactly one side, or ray. Their interiors are on opposite sides of that shared ray, so the inside of one angle doesn’t overlap the inside of the other. The middle letter in an angle name tells us which point is the vertex.
Find adjacent angles in a diagram
Look at and . They meet at , and their shared side is the ray from through . The first angle opens to the left and the second opens upward. They lie on opposite sides of the shared ray, so they’re adjacent.
We can go around the vertex the same way. and share the ray through ; and share the ray through ; and and share the ray through . That gives us four pairs of adjacent angles in the diagram.
Angles 1 and 2 share the vertex but no side, so they’re nonadjacent. They’re also vertical angles because they lie opposite each other where the two lines cross.
What can we tell from the names alone?
and share vertex and the ray through . They’re adjacent if the interiors lie on opposite sides of that ray. If both angles open to the same side of that ray, their interiors overlap, so we need the diagram to decide. The same idea applies to and , which share the ray from through .
and name the same angle because both rays and the vertex match. and have different vertices, and , so they’re nonadjacent.
